0    Introduction

    In order to improve the whole efficiency of the electronic equipment, the search for more efficient soft switching technique has been developed. For switch such as IGBT,the zero- current switching(ZCS) and zero-current transition(ZCT)technology have been frequently used, because this method can reduce the current rapidly when IGBT turns off, therefore reducing the energy loss caused by the tail current [1][2][3][4][5].

    But the zero-current switching circuit that mostly used is not input-out-isolated, so the application in the practice has not been generalized. This paper proposed the ZCS technique realized by the halfª² bridge converter, both the main switch and auxiliary switch in the topology work in softª² switching state, the turn-on current stress and turn-off voltage stress is small.

1    Operational Principles

    Fig.1 shows the circuit diagram of the half-bridge converter. In the schematic, L_r1 to L_r4 are resonant inductors, the C_r is resonant capacitor, S₁ and S₂ are main switches, S₃ and S₄ are auxiliary switches, D₁ to D₄ are anti-parallel diodes in the switches, C_s1 to C_s4 are snubber-capacities. The circuit is the conventional halfª² bridge topology incorporating the auxiliary resonant tank that composed of switches S₃ and S₄. The zero current switching state can be obtained by controlling the work sequence of the switches. Fig.2 is the theoretical waveforms when the converter in steady-state operation.

Fig.1 Schematic of the ZCS PWM half-bridge converter

Fig.2 the main ideal waveform

    The ideal analyses are given for all modes of the circuit, there are some differences between the theoretical analyses and practical condition because the following assumptions are made:

    1)The link capacitor C₁ and C₂ in the half-bridge are so large that the voltage of the capacitors can be treated as a constant in each switching period.

    2)The capacitor C₃ is so large that there is little voltage reduction in C₃.

    3)The output filter inductor L_f is large enough that the current through it can be treated as a constant in each switching period.

    4)The S₁,S₂,S₃ and S₄ are ideal switches.

    5)The snubber-capacity C_s1,C_s2,C_s3 and C_s4 are much smaller than the resonant capacity C_r, so the influence on the resonance can be disregarded.

    Additionally, the parameter meets the following:

    6)The value of the leakage inductor L_k of the transformer is much larger than that of the resonant inductor.

    7)The value of L_r1,L_r2,L_r3 and L_r4 is L_r.

    8)The value of C_s1,C_s2,C_s3 and C_s4 is C_s.

    9)The link capacitor C₁ and C₂ have the same values of C.

    Just as conventional ZCS DC£­DC converter circuit, the circuit can easily realize ZCS in light load condition. So the research and experiment in this paper are mainly concentrated in heavy load condition. To heavy load condition, the work process of the circuit can be sorted as following nine models:

    Model 1¡² t₀¡«t₁¡³ At t₀, the switch S₁ turns on, but the power is not delivered to the load because the transformer is shorted, the electric energy is only transfer to the leakage inductor L_k and resonant inductor L_r. So the current increase gradually from zero to I_o/n (the n is the turn ratio of the transformer), the turn-on state of switch is zero current. The current conducting through S₁ increases linearly with the slope of U_in/2(L_k£«L_r), therefore the time interval of this model is given by

    t₁£­t₀=2(L_r£«L_k)I_o/(nU_in) (1)

    Model 2¡² t₁¡«t₂¡³ At t₁, when the current through S₁ is equal to I_o/n, the power energy is delivered to the load, the circuit is in half-bridge converter PWM state. Then the current through S₁ maintains to be I_o/n.

    Model 3¡² t₂¡«t₃¡³ At t₂, the auxiliary switch S₃ turns on in zero-current state. The resonant tank composed of L_r1, L_r3 and C_r begins to work. If the voltage of C_r at t₂ is u_Cr(t₂), the voltage of C_r can be expressed as

    u_Cr=u_Cr(t₂)cos¡² ¦Ø ₁(t£­t₂)¡³ (2)

The current of L_r1 can be expressed as

    i_Lr1=I_m1sin¡² ¦Ø ₁(t£­t₂)¡³ (3)

where the resonant frequency ¦Ø ₁ is given by

    ¦Ø ₁= (4)

The maximum current of the L_r1 can be given by

    I_m1=u_Cr(t₂)/Z_LC (5)

The impedance of the resonant Z_LC can be given by

    Z_LC= (6)

    Model 4¡² t₃¡«t₄¡³ At t₃, the current through the resonant tank increases to I_o/n, the current through S₁ decreases to zero, the anti-parallel diode begins to work, because the current through resonant tank increases from zero, according to

    i(t₃)=I_o/n (7)

The time interval can be derived from

    t₃£­t₂= (8)

    Model 5¡² t₄¡«t₅¡³ At t₄, when turning off the S₁, the S₁ is in zero-current state, but the anti-parallel diode is still in conducting state. The current through resonant tank decreases from I_m1 to I_o/n, The total time interval of model 4 and model 5 is

    t₅£­t₃=2 (9)

By the equation (2) and (9), the voltage of C_r at t₅ can be expressed as

    u_Cr(t₅)=£­ U_Cr(t₂) (10)

    Model 6¡² t₅¡« t₆¡³ At t₅, the current of resonant tank decreases to I_o/n, the diode D₁ turns off naturally, then the current through the resonant tank will keep to be I_o/n, the voltage of S₁ begins to increase, while the voltage of S₂ to decrease.Because the capacitor discharges in constant current, so the voltage of resonant capacitor can be given as

    u_Cr(t)£­ u_Cr(t₅)= (11)

    From the equation(11) we can see that the voltage value of resonant capacitor increases gradually, at t₆, to U_in/2. From equation (10) and (11), we know that the time interval of this model can be expressed as

    t₆£­t₅= (12)

    Model 7¡² t₆¡« t₇¡³ At t₆, the voltage of C_r begins to increase from U_in/2, the rectifier composed of D₅ to D₈ begins to conduct, the voltage of S₂ continues to decrease. The resonant network is composed of inductor L_r3, resonant capacitor C_r and leakage inductor L_k, and the network cooperation with link capacitor C₁, the initial state of the resonant network is

    i_Lr3(t₆)= (13)

    u_Cr(t₆)= (14)

    Therefore this model should meet the following equation:

    u_Cr(t)=cos¡² ¦Ø ₂(t£­ t₆)¡³ £« sin¡² ¦Ø ₂(t£­ t₆)¡³ (15)

    i_Lr(t)=cos¡² ¦Ø ₂(t£­ t₆)¡³ £­ sin¡² ¦Ø ₂(t£­ t₆)¡³ (16)

where

    ¦Ø ₂= (17)

    At t₇, when the voltage of C_r is Vin, the D₂ begins to work, the voltage of the leakage inductor is fixed at (L_k£« L_r)U_in/L_k. From equation (15) and (16). We can see that the time interval of model 7 can be given by

    t₇£­t₆=arctan  (18)

    Model 8¡² t₇¡« t₈¡³ At t₇, the voltage of S₂ decreases to zero, the anti-parallel diode D₂ begins to work, the current through the transformer will be reduced to zero by the capacitor C₂.

    In this model, the current of L_r3 should meet the following equation:

    i_Lr3(t)=i_Lr(t₇)cos¦Ø ₃t£­ sin¦Ø ₃t (19)

where

    ¦Ø ₃= (20)

The current of leakage inductor can be given by

    i_k(t)= £­ i_Lr(t₇) (21)

The voltage of C_r should meet the following equation:

    u_Cr(t)=¡Á (22)

The time interval of this model can be given by

    t₈£­ t₇= (23)

    Model 9¡² t₈¡« t₁₀¡³ At t₈, the current through the transformer is zero. The resonant tank composed of C_r,L_r3 and L_r2 will begin to work, and the current through L_r3 will change the direction. At t₉, when turning off S₃, the S₃ is in ZCS model. After half of the resonant period, the current of L_r3 decreases back to zero and the anti-parallel diode D₃ turns off natu rally. The time interval of this model can be given by

    t₁₀£­ t₈= (24)

    The work process of S₂ is accordant with above, so in this paper the work process of S₁ is mainly discussed.

£¨ a£© ¡² t₀¡« t₁¡³ £¨ b£© ¡² t₁¡« t₂¡³

£¨ c£© ¡² t₂¡« t₃¡³ £¨ d£© ¡² t₃¡« t₅¡³

£¨ e£© ¡² t₅¡« t₆¡³ £¨ f£© ¡² t₆¡« t₇¡³

£¨ g£© ¡² t₇¡« t₈¡³ £¨ h£© ¡² t₈¡« t₁₀¡³

Fig.3 The equivalent circuits of the work process by S1

2    The Discussion to the Circuit Model

2.1    The Duty Ratio Loss

    The duty ratio loss is concentrated in time interval t₀ to t₁, therefore the duty ratio loss is

    D_loss= (25)

where Ts is the switch cycle period.

2.2    Minimum Duty Ratio

    To ensure soft switching off, there should be enough time for the current of S₁ to decrease to zero before the switch turns off. From model 3, equation (8), we can deduce the minimum duty ratio is

    D_min= (26)

2.3    Soft Commutation Conditions

    1)From the analysis for model 4, 5 and equation (8) and (9), we can see that, if there is enough time for S₁ to realize turning at zero current, the maximum current of the resonant network must meet the following expression:

    I_m1= (27)

    2)If the output current I_o is small, and the I_o meet the following expression:

     < U_in (28)

    From equation (15), we know that the voltage of C_r will not increase to U_in, the D₂ would not conduct, the time interval of model 7 would delay until the current of the L_k decreases to zero, therefore the model 8 would disappeared. But still the IGBT is switched in ZCS, and the D₃ turns off naturally.

    3)From the above analysis to topology, we can see that in the topology, if the maximum current is larger enough to meet the expression (27), and the time t₄ correspended to main switch turning off satisfies the following condition:

    t₂£« < t₄< t₂£« (29)

    and the time t₉ correspended to auxiliary switch turning off meets the following condition:

    t₈< t₉< t₂£« (30)

    then the main switch and auxiliary switch are all well in zero-current switch. The resonant inductors L_r1 to L_r4 do not only slow down the increasing rate of the current when switching on, but also realize soft-switch when the switch turns off. This is realized through making the anti-parallel diode conduct by the resonant network.

3    Experiment Results

    To verify the operation and the performance of the proposed improved half-bridge converter, the 1 kW prototype has been implemented, the following are main parameters

    Input voltage U_in, 232 V;

    Output voltage, 80 V;

    Output resistance value, 6 ¦¸ ;

    Switching frequency f_s, 80 kHz;

    Leakage inductor value, 5 ¦Ì H;

    The resonant inductor, 1 ¦Ì H;

    Resonant capacitor is 72 nF.

    Fig.4 is the voltage and current waveform when the switch working. Fig.4(a) is for the main switch and fig.4(b) for auxiliary switch. From the waveform presented, we can see that main switch and auxiliary switch are well done in zero-current switch, and the stress of the current and voltage is small.

(a) The voltage and current waveform of main switch

(The scale of current is 5A/div, that of time is 1¦Ì s/div)

(b) The voltage and current waveform of auxiliary switch

(The scale of current is 10A/div, that of time is 2.5¦Ì s/div)

Fig.4 The main experimental waveform

(The abscissa is time, and the ordinate is voltage and current, the scale of the voltage is 50V/div and the voltage wave form is marked by ¡° ¡õ ¡± )

4    Conclusion

    From the theoretical analysis and experiment result, we can see that the topology has following feature:

    ¡ª Because the resonant inductors L_r1 to L_r4 are in series with switches, they cooperate with leakage inductor L_k that slow down the change rate of the current. Therefore the current stress has been reduced when the switches turn on.

    ¡ª The resonant inductors L_r1 to L_r4 finish the soft switch in cooperation with the Cr.

    ¡ª The anti-parallel diodes work in soft-switch state.

    ¡ª The topology is not strict with the leakage inductor.

    ¡ª The topology is adapted to improve the IGBT work frequency.